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Salome Zurabishvili has been sworn into office as Georgia's first woman president amid continued denunciations by the opposition that her election was rigged.

In her inaugural speech on December 16, Zurabishvili vowed to reconcile political divisions and deepen ties with NATO and the European Union.

"As the Georgian president backed by our strategic partner, the United States, and European friends, I will make every effort to promote our country's integration process into NATO and the EU," she said.

She also urged Russia to respect international law if it wants to normalize relations with its neighbors. Tbilisi’s relations with Moscow remain tense following a five-day war in 2008.

"Russia should understand that, if it wants to be a full-fledged member of the international community and normalize relations in the region, it should prove the recognition of international legal norms by words and by deeds. This is mandatory for establishing an equal and peaceful relationship with its neighbors," she said.

She added that Russia was continuing its "unacceptable" occupation of two Georgian regions, South Ossetia and Abkhazia.

Russia-backed separatists have controlled the regions since the 2008 war, and Moscow has recognized them as independent states. Only a handful of countries have followed suit.

The inauguration ceremony was held at an 18th-century palace in the town of Telavi, about 100 kilometers east of the capital, Tbilisi.

More than 1,800 Georgian and foreign guests attended the event, including Armenian President Armen Sarkisian and French former President Nicolas Sarkozy.

A French-born former foreign minister of Georgia, the 66-year-old Zurabishvili won a November 28 runoff vote for the presidency with 59.5 percent of the vote. She was backed by the ruling Georgian Dream party.

Zurabishvili’s rival in the runoff, Grigol Vashadze of the opposition United National Movement, received 40.5 percent of the vote.

But opposition parties have refused to accept the results, pointing to instances of alleged fraud in the runoff vote.

On December 16, opposition supporters tried to hold a demonstration in Telavi, but police blocked their convoy of cars and buses on a road leading from Tbilisi to the town.

WATCH: Georgian police prevented a convoy of opposition supporters from reaching the historic town of Telavi, where Salome Zurabishvili was sworn in on December 16.

Clashes were reported between police and protesters as they tried to break through police ranks.

"Georgian Dream has taken away our constitution, our state institutions, our freedom of expression," Vashadze later told journalists.

International monitors said the runoff vote was "competitive," but Zurabishvili "enjoyed an undue advantage," citing the misuse of administrative resources that "blurred the line between party and state."